def test_curvature(self):
group = self.matrix_so3
metric = InvariantMetric(group=group)
x, y, z = metric.normal_basis(group.lie_algebra.basis)
result = metric.curvature_at_identity(x, y, x)
expected = 1.0 / 8 * y
self.assertAllClose(result, expected)
tan_a = gs.stack([x, x])
tan_b = gs.stack([y] * 2)
result = metric.curvature(tan_a, tan_b, tan_a)
self.assertAllClose(result, gs.array([expected] * 2))
point = group.random_uniform()
translation_map = group.tangent_translation_map(point)
tan_a = translation_map(x)
tan_b = translation_map(y)
result = metric.curvature(tan_a, tan_b, tan_a, point)
expected = translation_map(expected)
self.assertAllClose(result, expected)
result = metric.curvature(y, y, z)
expected = gs.zeros_like(z)
self.assertAllClose(result, expected)
def test_curvature(self, group, tangent_vec_a, tangent_vec_b,
tangent_vec_c, expected):
metric = InvariantMetric(group)
result = metric.curvature(tangent_vec_a,
tangent_vec_b,
tangent_vec_c,
base_point=None)
self.assertAllClose(result, expected)
def test_curvature_translation_point(self, group, tangent_vec_a,
tangent_vec_b, tangent_vec_c, point,
expected):
metric = InvariantMetric(group)
translation_map = group.tangent_translation_map(point)
tan_a = translation_map(tangent_vec_a)
tan_b = translation_map(tangent_vec_b)
tan_c = translation_map(tangent_vec_c)
result = metric.curvature(tan_a, tan_b, tan_c, point)
expected = translation_map(expected)
self.assertAllClose(result, expected)